At a certain simple rate of interest, a given sum amounts to Rs 13920 in 3 years, and to Rs 18960 in 6 years and 6 months. If the same given sum had been invested for 2 years at the same rate as before but with interest compounded every 6 months, then the total interest earned, in rupees, would have been nearest to:
Show Hint
- \(3096\)
- \(3221\)
- \(3180\)
- \(3150\)
The Correct Option is B
Solution and Explanation
Step 1: Find the principal and simple interest rate. Amount after 3 years: \[ A_1 = 13920. \] Amount after 6.5 years: \[ A_2 = 18960. \] Time difference: \[ 6.5 - 3 = 3.5 \text{ years}. \] Extra interest in these 3.5 years: \[ \Delta I = A_2 - A_1 = 18960 - 13920 = 5040. \] So simple interest per year: \[ \text{SI per year} = \frac{5040}{3.5} = 1440. \] Interest for first 3 years: \[ \text{SI}_{3\text{ yrs}} = 1440 \times 3 = 4320. \] Hence principal: \[ P = A_1 - \text{SI}_{3\text{ yrs}} = 13920 - 4320 = 9600. \] Rate of interest: \[ R = \frac{\text{SI per year}}{P} \times 100 = \frac{1440}{9600} \times 100 = 15% \text{ p.a.} \]
Step 2: Compound interest for 2 years, half-yearly. Principal: \[ P = 9600. \] Rate per half-year: \(r = \frac{15\%}{2} = 7.5% = 0.075\). Number of half-yearly periods in 2 years: \[ n = 2 \times 2 = 4. \] Amount: \[ A = P\left(1 + \frac{r}{100}\right)^n = 9600 \times (1.075)^4. \] Approximate: \[ (1.075)^2 \approx 1.1556,\quad (1.1556)^2 \approx 1.335\ (\text{approximately}), \] so \[ A \approx 9600 \times 1.335 \approx 12820. \] Compound interest: \[ \text{CI} = A - P \approx 12820 - 9600 = 3220 \text{ (approximately)}. \] Among the given options, the nearest value is \(3221\). Therefore, the total interest would have been approximately: \[ \boxed{3221}. \]
Top Questions on SI & CI
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In the dynamic realm of creativity, artists often find themselves at the crossroads between drawing inspiration from diverse cultures and inadvertently crossing into the territory of cultural appropriation. Inspiration is the lifeblood of creativity, driving artists to create works that resonate across borders. In a globalized era of the modern world, artists draw from a vast array of cultural influences. When approached respectfully, inspiration becomes a bridge, fostering understanding and appreciation of cultural diversity. However, the line between inspiration and cultural appropriation can be thin and easily blurred.
Cultural appropriation occurs when elements from a particular culture are borrowed without proper understanding, respect, or acknowledgment. This leads to the commodification of sacred symbols, the reinforcement of stereotypes, and the erasure of the cultural context from which these elements originated. It is essential to recognize that the impact of cultural appropriation extends beyond the realm of artistic expression, influencing societal perceptions and perpetuating power imbalances.- CAT - 2025
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